Rotation search has become a core routine for solving many computer vision problems. The aim is to rotationally align two input point sets with correspondences. Recently, there is significant interest in developing globally optimal rotation search algorithms. A notable weakness of global algorithms, however, is their relatively high computational cost, especially on large problem sizes and data with a high proportion of outliers. In this paper, we propose a novel outlier removal technique for rotation search. Our method guarantees that any correspondence it discards as an outlier does not exist in the inlier set of the globally optimal rotation for the original data. Based on simple geometric operations, our algorithm is deterministic and fast. Used as a preprocessor to prune a large portion of the outliers from the input data, our method enables substantial speed-up of rotation search algorithms without compromising global optimality. We demonstrate the efficacy of our method in various synthetic and real data experiments.